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Results tagged with hamiltonian-mechanics
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user 19276
21
votes
Is there a high level reason why the inverse square law of gravitation yields periodic orbit...
There are:
Bertrand’s theorem, which says that the isotropic oscillator and Kepler potentials are the only analytic radial ones all of whose nonrectilinear bounded orbits are closed. (Recommendation …
- 31.5k
5
votes
Accepted
Contradiction between fixed points of a hamiltonian diffeomorphism of a torus and quasi-peri...
1) is correct: by saying “hamiltonian diffeomorphism of” you imply that the torus has a symplectic structure $\omega$ and the diffeo is (something like) time 1 flow of a hamiltonian vector field $X$: …
- 31.5k
3
votes
Accepted
Practical example of Hamiltonian reduction
The reduction you require is a (very) special case of Marsden-Weinstein (1974). Your one constant of the motion, say $\psi$, is the moment map of an action of the additive group $G=\mathbf R$ on the s …
- 31.5k